The right to free speech is protected under the First Amendment of the United States Constitution. A statute is deemed to be overly broad and violative of the Constitution if it prohibits speech that is merely offensive to certain persons. The prohibited speech must constitute "fighting words," which are defined as words that have a direct tendency to cause acts of violence by the person to whom the words are directed. Fighting words include profane, obscene, and threatening words.
Nothing on any of these T-shirts, or really on any T-shirt period, could ever qualify as "fighting words".

Local governments have no right to implement an ordinance like this, irrespective of what it's own community thinks and wants. The right for one store owner to make a meager profit off of shameless garbage like this completely supersedes the desire of an entire community to project a "family friendly" image.